This application is related to Japanese patent application No. 2000-042949 filed on Feb. 21, 2000, whose priority is claimed under 35 USC xc2xa7119, the disclosure of which is incorporated by reference in its entirety.
1. Field of the Invention
The present invention relates to an active inductor and, more particularly, to an active inductor with its inductance electrically controllable, which comprises an MOSFET and a single capacitor for applications to RF (radio frequency) integrated circuits, high frequency VCOs and the like.
2. Description of the Prior Art
In general, inductors are implemented as passive elements employing metal spirals or bonding wires for use in filters, oscillators, RF tuned circuits and the like.
An active inductor with its inductance electrically controllable is disclosed in Japanese Unexamined Patent Publication No. Sho 63(1988)-219150 (Reference 1). The active inductor employs two cascade-connected FETs (field effect transistors) and a feedback resistor for suppression of a reduction in the inductance thereof and for size reduction thereof. This active inductor is also disclosed in IEEE Transactions on Microwave Theory and Techniques, Vol. 37, No. 12 (December 1989), pp. 1979-1984.
The active inductor (not shown) disclosed in Reference 1 has an output inductance Zo expressed as follows:
Zo≈(1+jxcfx89xc2x7Cgsxc2x7R)/gm
wherein Cgs is the gate-source capacitance of the FETs, gm is the transconductance of the FETs, R is a feedback resistance, and xcfx89 is a resonant frequency. In the active inductor, the gate-source capacitance Cgs of the FETs serves to provide the inductance.
An active inductor disclosed in Japanese Unexamined Patent Publication No. Hei 2(1990)-205107 (Reference 2) is a modification of the active inductor of Reference 1, which employs an FET instead of the feedback resistor R. In this case, the feedback resistance R is expressed as R=1/gmf, wherein gmf is the transconductance of the feedback transistor.
An active inductor disclosed in Japanese Unexamined Patent Publication No. Hei 8(1996)-181571 (Reference 3) comprises three FETs and four capacitors C. The capacitors are used for DC isolation of the transistors.
An active inductor disclosed in Japanese Unexamined Patent Publication No. Hei 8(1996)-274584 (Reference 4) comprises a source-grounded FET, two cascade-connected FETs, three capacitors C and a resistor R.
In general, the high frequency operation range of an active inductor is limited by stray capacitances that resonate with an equivalent inductor.
FIG. 7(a) is a diagram illustrating a high frequency equivalent circuit of the active inductor, and FIG. 7(b) is a diagram illustrating an output impedance characteristic with respect to the frequency of the active inductor.
As shown in FIG. 7(b), a peak Zo in the output impedance characteristic is observed at a resonance frequency xcfx89o, which is given by the following expression:
xcfx89o=1/(Leqxc2x7Cp)xc2xd
wherein Leq is an inductance, and Cp is a stray capacitance, which is expressed as follows for the circuit of Reference 1.
Cp=Cgsxc2x7(xcfx89xc2x7Cgs/gm)2+Cm
wherein Cm is a layout-dependent parasitic capacitance. The parasitic capacitance should be minimized to extend the frequency range of the inductor.
The active inductors having the circuit configurations of References 1 and 2 are problematic in that the inductance thereof is determined by the gate-source capacitance Cgs of the FETs.
The active inductors having the circuit configurations of References 3 and 4 are problematic in that the capacitors C should be additionally employed for DC isolation of the FETs. This results in complication and size increase of the circuits constituting the active inductors.
In view of the foregoing, the present invention is directed to an active inductor which comprises an MOSFET and a single capacitor and features a reduced size and an excellent frequency response characteristic as compared with the conventional active inductors.
In accordance with the present invention, there is provided an active inductor comprising: an MOSFET having a gate, a drain serving as an output. terminal and a grounded source, the MOSFET having a transconductance gm1; and a capacitor having opposite ends, one of which is grounded and the other of which is connected to the gate of the MOSFET and to a voltage-controlled constant current source having a transconductance gm, the capacitor having a capacitance C; the active inductor being operative with a small-signal output impedance Zo between the output terminal and the ground expressed as Zo=jxcfx89G{C/(gm1xc2x7gm)} (wherein xcfx89 is an angular frequency) and with an inductance Leq expressed as Leq={C/(gm1xc2x7gm)}.
With this arrangement, the active inductor can have an excellent frequency response characteristic and a reduced size as compared with the conventional active inductors.